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2 years ago

Please Answer As Soon As Possible

Mathematics

2 answers:

Doss [256]2 years ago

7 0

Mean is the easiest way to get your answer

taurus [48]2 years ago

5 0

Answer:

mean is the best way

Step-by-step explanation:

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in exercises 15-20 find the vector component of u along a and the vecomponent of u orthogonal to a u=(2,1,1,2) a=(4,-4,2,-2)

Nimfa-mama [501]

Answer:

The component of $\vec u$ orthogonal to $\vec a$ is $\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)$ .

Step-by-step explanation:

Let $\vec u$ and $\vec a$ , from Linear Algebra we get that component of $\vec u$ parallel to $\vec a$ by using this formula:

$\vec u_{\parallel \,\vec a} = \frac{\vec u \bullet\vec a}{\|\vec a\|^{2}} \cdot \vec a$ (Eq. 1)

Where $\|\vec a\|$ is the norm of $\vec a$ , which is equal to $\|\vec a\| = \sqrt{\vec a\bullet \vec a}$ . (Eq. 2)

If we know that $\vec u =(2,1,1,2)$ and $\vec a=(4,-4,2,-2)$ , then we get that vector component of $\vec u$ parallel to $\vec a$ is:

$\vec u_{\parallel\,\vec a} = \left[\frac{(2)\cdot (4)+(1)\cdot (-4)+(1)\cdot (2)+(2)\cdot (-2)}{4^{2}+(-4)^{2}+2^{2}+(-2)^{2}} \right]\cdot (4,-4,2,-2)$

$\vec u_{\parallel\,\vec a} =\frac{1}{20}\cdot (4,-4,2,-2)$

$\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)$

Lastly, we find the vector component of $\vec u$ orthogonal to $\vec a$ by applying this vector sum identity:

$\vec u_{\perp\,\vec a} = \vec u - \vec u_{\parallel\,\vec a}$ (Eq. 3)

If we get that $\vec u =(2,1,1,2)$ and $\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)$ , the vector component of $\vec u$ is:

$\vec u_{\perp\,\vec a} = (2,1,1,2)-\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)$

$\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)$

The component of $\vec u$ orthogonal to $\vec a$ is $\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)$ .

4 0

3 years ago

Ill give brainliest

yuradex [85]

Answer:

y-coordinate is 5 or -1.

Step-by-step explanation:

Point A is at (x, 2) and B is at (x+6, 2). Since AB must lie on the line y=2 and be 6 units long. Point C is on the line x = -3 . So let C be at (-3, y).

Since ΔABC is a right angle, then point C must have the same x-coordinate as point A. Therefore, A(-3, 2) and B(2, 2).

The area of ΔABC is 6. So,

9 = 1/2 (b)(h)

where b is the base and h is the height.

so b = 6 and h = AC

Solving this for C gives

9 = 1/2 (6)(AC)

18/6 = AC

3 = AC

9 = 1/2 (6)(AC)

18/6 = AC

3 = AC

Point C must lie 3 units above point A or 3 units below the point A. If it lies 3 units above, then it has a y-coordinate of 2 + 3 = 5.

If it lies 3 units below, it has a y-coordinate 2 - 3 = -1.

Therefore, y-coordinate is 5 or -1.

Step-by-step explanation:

5 0

3 years ago

Please help! I currently have a C- in Math and I need an A before summer

san4es73 [151]

Its 12. I hope I help

6 0

3 years ago

Read 2 more answers

LIONS SPEND ABOUT 5/6 OF THEIR DAY SLEEPING. HOW MANY HOURS A DAY DOES A LION SLEEP? WRITE AN EQUATION TO MODE YOUR WORK.

Alenkasestr [34]

So a day is 24 hours
24/6=4
4*5=20
so they spend 20 hours a day sleeping
here’s a full on equation
(24/6)*5

4 0

3 years ago

Amy can mop the store in 30 minutes. James can mop the store in 45 minutes. How long would it take them if they worked together?

zavuch27 [327]

Solve the equation 1/30 + 1/45 = 1/x

where x is the required time

multiply thru by 90x:-

3x + 2x = 90

x = 90 / 5 = 18

answer 18 minutes

5 0

3 years ago